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For various reasons. Read an introductory calculus book; they are usually full of examples that have practical applications.

One common use of differentiation (derivation) is to find the maximum or minimum of some function. A maximum or minimum can occur (a) at the endpoints of the interval under consideration, (b) at a point where the derivative is zero, (c) at a point where the derivative is not defined. This, obviously, requires differentiation.

Integration can be used to find areas and volumes, or, more generally, the area under a curve that might not necessarily represent an area in the geometric sense. For example, work = force x distance - but what happens if the force changes while you move? This "variable product" is equivalent to finding an area under a curve.

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Q: Why do you differentiate and integrate?
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